Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking |
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Authors: | Michael Codish Michael Frank Avraham Itzhakov Alice Miller |
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Affiliation: | 1.Department of Computer Science,Ben-Gurion University of the Negev,Be’er Sheva,Israel;2.School of Computing Science,University of Glasgow,Glasgow,Scotland |
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Abstract: | The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set \(\mathcal {R}(3,3,3;13)\) consisting of 78,892 Ramsey colorings. |
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